The WLSEs Of Parametric Functions Under A Multiple Partitioned Linear Regression Model

For the parameter estimations under a linear model,the weighted least-squares es-timator (WLSE) is one of the commonly used methods.Many researchers have done a great amount of research work for the WLSEs of parametric functions under a linear re-gression model,and a lot of good results were presented.However, many problems still need to be further study.In this article,the necessary and sufficient conditions for the WLSE of parametric functions K1β1+…+Kmβm under a multiple partitioned linear model M={y,X1β1+ …+Xmβm,σ2∑} to be the sum of the WLSEs of Kiβi under the m small models Mi= {y,Xiβi,σ2∑),i=1,2,…,m,and for the WLSEs of parametric functions Kiβi under the linear model M to be equal to the WLSEs of parametric function Kiβi under its small model Mi,i=1,2,…,m are derived.Some statistical properties about the WLSEs of parametric functions are also described.